Nuprl Lemma : geo-triangle_functionality
∀e:HeytingGeometry. ∀a1,a2,b1,b2,c1,c2:Point. (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1 # b1c1 ⇐⇒ a2 # b2c2))
Proof
Definitions occuring in Statement :
geo-triangle: a # bc,
heyting-geometry: HeytingGeometry,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
guard: {T},
and: P ∧ Q,
heyting-geometry: HeytingGeometry,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ
Latex:
\mforall{}e:HeytingGeometry. \mforall{}a1,a2,b1,b2,c1,c2:Point.
(a1 \mequiv{} a2 {}\mRightarrow{} b1 \mequiv{} b2 {}\mRightarrow{} c1 \mequiv{} c2 {}\mRightarrow{} (a1 \# b1c1 \mLeftarrow{}{}\mRightarrow{} a2 \# b2c2))
Date html generated:
2020_05_20-AM-10_32_53
Last ObjectModification:
2020_01_13-PM-04_13_53
Theory : euclidean!plane!geometry
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